o
    *Î®cð‚  ã                   @   s˜  d dl mZ d dlmZmZmZmZ d dlmZm	Z	m
Z
mZmZmZmZmZ d dlmZ d dlmZ d dlmZmZ d dlmZmZmZmZmZmZmZmZ d dl m!Z!m"Z"m#Z# d d	l$m%Z% d d
l&m'Z' d dl(m)Z)m*Z*m+Z+m,Z,m-Z- d dl.m/Z/m0Z0 d dl1m2Z2 d dl3m4Z4 d dl5m6Z6 d dl7m8Z8 d dl9m:Z:m;Z; d dl<m=Z= d dl>m?Z? d dl m@Z@ d dlmAZA d dlBmCZCmDZDmEZE dd„ ZFdd„ ZGdd„ ZHdd„ ZIdd „ ZJeCd!d"„ ƒZKd#d$„ ZLd%d&„ ZMd'd(„ ZNd)d*„ ZOd+d,„ ZPd-d.„ ZQd/d0„ ZRd1d2„ ZSd3d4„ ZTd5d6„ ZUd7d8„ ZVeEd9d:„ ƒZWd;d<„ ZXd=d>„ ZYd?d@„ ZZdAdB„ Z[dCdD„ Z\dEdF„ Z]dGdH„ Z^eCdIdJ„ ƒZ_dKdL„ Z`eCdMdN„ ƒZadOdP„ ZbdQdR„ ZcdSdT„ ZddUdV„ ZeeEdWdX„ ƒZfdYS )Zé    )ÚExpr)Ú
DerivativeÚFunctionÚLambdaÚexpand)ÚEÚIÚRationalÚcompÚnanÚooÚpiÚzoo)ÚEq)ÚS)ÚSymbolÚsymbols)ÚAbsÚadjointÚargÚ	conjugateÚimÚreÚsignÚ	transpose)ÚexpÚ	exp_polarÚlog)Úsqrt)Ú	Piecewise)ÚacosÚatanÚatan2ÚcosÚsin)Ú
DiracDeltaÚ	Heaviside)ÚIntegral)ÚMatrix)ÚFunctionMatrix)ÚMatrixSymbol)ÚImmutableMatrixÚImmutableSparseMatrix)ÚSparseMatrix)ÚInterval)Ú	unchanged)ÚArgumentIndexError)ÚXFAILÚraisesÚ_both_exp_powc                 C   s   t |  ¡ | ¡ dƒS )z7Check whether two complex numbers are numerically closegíµ ÷Æ°>)r
   Ún)ÚaÚb© r7   úV/tmp/pip-target-vg8gfxp4/lib/python/sympy/functions/elementary/tests/test_complexes.pyÚN_equals   s   r9   c                  C   sü  t dƒ\} }t ddd\}}tddd}tddd}ttƒtu s"J ‚ttƒtu s*J ‚tt ƒt u s4J ‚tdƒdks<J ‚td	ƒd	ksDJ ‚td
ƒd
ksLJ ‚ttƒtksTJ ‚tt ƒt ks^J ‚tt| ƒseJ ‚t| t ƒt| ƒ ksrJ ‚t|t ƒdks|J ‚t|ƒ|ks„J ‚t|t ƒt| ksJ ‚t|ƒdks˜J ‚t| | ƒt| ƒt|ƒ ks¨J ‚t| | ƒt| ƒ| ks¶J ‚tt| ƒƒt| ƒksÂJ ‚tdt ƒdksÌJ ‚t| t ƒt| ƒksØJ ‚t| |t  ƒt| ƒt|ƒ ksêJ ‚t| |t  ƒt| ƒksøJ ‚tt	dt ƒƒt	dƒksJ ‚tdt d ƒj
dddksJ ‚tt| ƒƒt| ƒks%J ‚tt| ƒƒt| ƒks2J ‚t| ƒ ¡ t| ƒdfksAJ ‚t|| |  ƒ |¡t||  ƒksUJ ‚t|| |  ƒ |¡t| t| ƒ kskJ ‚tt||t  ƒƒ|d |d  td	dƒ tt||ƒd ƒ ksŽJ ‚t|d|t   ƒd| ksŸJ ‚td	t||t  ƒ d ƒ|d |d  td	dƒ tt||ƒd ƒ d tj ksËJ ‚t| ƒ t¡| tjt| ƒ  ksÞJ ‚| t|ƒ  tt¡| | tjt|ƒ  ksöJ ‚tddd}tddd}tdƒ} t|ƒjsJ ‚t| ƒjd u sJ ‚t|ƒjdu s"J ‚ttjƒtju s-J ‚t dƒ\}}}	td||ƒ}
t|
ƒtj|
t|
ƒ  ksJJ ‚td	dt  dgddt ggƒ}
t|
ƒtd	dgddggƒkskJ ‚td	dt  ddt  gddt ggƒ}
t|
ƒtd	dgddggƒksJ ‚tdd„ tdƒD ƒƒ}t|ƒtg d¢g d¢g d¢g d¢g d¢gƒ t d¡ksºJ ‚t|ƒtg d ¢g d ¢g d ¢g d ¢g d ¢gƒ t d¡ksÙJ ‚tddt ||f||t  ƒƒ}t|ƒtg d!¢g d"¢g d#¢gƒksüJ ‚d S )$Núx,yúa,bT©ÚrealÚrÚi©Ú	imaginaryr   é   éÿÿÿÿé   ©Úcomplexé   é   r5   ©Ú	algebraicÚt©ÚtranscendentalÚxFún m lÚAéýÿÿÿc                    s"   g | ]‰ ‡ fd d„t dƒD ƒ‘qS )c                    s   g | ]
}d ˆ  |t   ‘qS )rD   ©r   ©Ú.0r?   ©Újr7   r8   Ú
<listcomp>m   s    z&test_re.<locals>.<listcomp>.<listcomp>é   ©Úrange)rT   r7   rU   r8   rW   m   s   " ztest_re.<locals>.<listcomp>rX   )r   r   r   r   r   )rD   rD   rD   rD   rD   )rH   rH   rH   rH   rH   )é   r[   r[   r[   r[   )é   r\   r\   r\   r\   )r   rB   rD   rG   rH   )r   r   r   )rB   rB   rB   )rD   rD   rD   )!r   r   r   r   r   r   r/   r   r   r   r   r   Úas_real_imagÚdiffr   r	   r#   r"   r   ÚHalfÚrewriteÚImaginaryUnitÚis_algebraicÚComplexInfinityÚNaNr*   r(   r+   r-   rZ   Úzerosr)   r   )rN   Úyr5   r6   r>   r?   rK   r4   ÚmÚlrP   ÚXr7   r7   r8   Útest_re   s˜    $"(,ÿ*
ÿ"4
ÿ&0  "("ü
üü
ü,rj   c                  C   sð  t dƒ\} }t ddd\}}tddd}tddd}ttƒtu s"J ‚ttt ƒtu s,J ‚tt t ƒt u s8J ‚tdƒdks@J ‚td	ƒdksHJ ‚td
ƒdksPJ ‚ttt ƒtksZJ ‚tt t ƒt ksfJ ‚tt| ƒsmJ ‚t| t ƒt| ƒksyJ ‚t|t ƒ|ksƒJ ‚t|ƒdks‹J ‚t|t ƒdks•J ‚t|ƒt | ks J ‚t| | ƒt| ƒt|ƒ ks°J ‚t| | ƒt| ƒks¼J ‚t| |t  ƒt| ƒ| ksÌJ ‚tt| ƒt ƒt| ƒksÚJ ‚tdt ƒd	ksäJ ‚t| t ƒt| ƒd	 ksòJ ‚t| |t  ƒt| ƒt|ƒ ksJ ‚t| |t  ƒt| ƒ| ksJ ‚tt	dt ƒƒt
d ks%J ‚tdt d ƒjdddks6J ‚tt| ƒƒt| ƒ ksDJ ‚tt| ƒƒt| ƒksQJ ‚t| ƒ ¡ t| ƒdfks`J ‚t|| |  ƒ |¡t||  ƒkstJ ‚t|| |  ƒ |¡t t||  ƒ ks‹J ‚tt||t  ƒƒ|d |d  td	dƒ tt||ƒd ƒ ks®J ‚t|d|t   ƒ|| ks¿J ‚td	t||t  ƒ d ƒ|d |d  td	dƒ tt||ƒd ƒ d ksèJ ‚t| ƒ t¡tj | t| ƒ  ksüJ ‚| t|ƒ  tt¡| tj|t|ƒ   ksJ ‚tddd}tddd}tdƒ} t|ƒjs,J ‚t| ƒjd u s6J ‚t|ƒjdu s@J ‚ttjƒtju sKJ ‚t dƒ\}}}	td||ƒ}
t|
ƒtjdt  |
t|
ƒ  kslJ ‚td	dt  dgddt ggƒ}
t|
ƒtddgddggƒksJ ‚td	dt  ddt  gddt ggƒ}
t|
ƒtddgddggƒks²J ‚tdd„ tdƒD ƒƒ}tdd„ tdƒD ƒƒ}t|ƒ  ¡ |ksÓJ ‚t!ddt"||f||t  ƒƒ}t|ƒtg d¢g d¢g d¢gƒksöJ ‚d S )Nr:   r;   Tr<   r>   r?   r@   r   rB   rC   rD   rE   rH   r5   rI   rK   rL   rN   FrO   rP   rQ   rG   éþÿÿÿc                 S   ó   g | ]}d d„ t dƒD ƒ‘qS )c                 S   s   g | ]}|t  | ‘qS r7   rR   rS   r7   r7   r8   rW   Ð   s    ú&test_im.<locals>.<listcomp>.<listcomp>rX   rY   rS   r7   r7   r8   rW   Ð   ó    ztest_im.<locals>.<listcomp>rX   c                 S   rl   )c                 S   s   g | ]}|‘qS r7   r7   rS   r7   r7   r8   rW   Ñ   s    rm   rX   rY   rS   r7   r7   r8   rW   Ñ   rn   )r   rB   rD   )#r   r   r   r   r   r   r   r/   r   r   r   r   r   r]   r^   r   r	   r$   r"   r`   r   ra   rb   rc   rd   r*   ÚOner(   r+   r,   rZ   r-   Úas_immutabler)   r   )rN   rf   r5   r6   r>   r?   rK   r4   rg   rh   rP   ri   ÚYr7   r7   r8   Útest_im~   s‚     &""(.ÿ*
ÿ".
ÿ(0( "("ÿ,rr   c            
      C   s¢	  t dƒdksJ ‚t dƒdksJ ‚t dt ƒtksJ ‚t dt ƒt ks%J ‚t dƒdks-J ‚t ddd	 ¡ dks9J ‚t tdd	 ¡ dksEJ ‚t tƒtu sMJ ‚t d
d
t  ƒ ¡ td
ƒd
d
t   d kseJ ‚t d
dt  ƒ ¡ t d
dt  ƒksyJ ‚t d
d
t  ƒ ¡ t dt ƒks‹J ‚t ttdtdƒ ƒƒƒdks›J ‚t tdtdƒ ƒƒtks©J ‚tdƒ} t | ƒj	du s¶J ‚t | ƒj
du s¿J ‚t | ƒjd u sÈJ ‚t | ƒjd u sÑJ ‚t | ƒjd u sÚJ ‚t | ƒjd u sãJ ‚t | ƒ ¡ t | ƒksïJ ‚t d|  ƒt | ƒksûJ ‚t d
|  ƒt | ƒksJ ‚t t|  ƒtt | ƒ ksJ ‚t dt |  ƒt t | ƒ ks)J ‚t t| ƒƒtt | ƒƒks8J ‚tddd}tddd}tddd}t d
| |  ƒt | ƒksYJ ‚t ||  ƒt | ƒ ksgJ ‚t || |  ƒt | ƒksvJ ‚tddd} t | ƒjdu s†J ‚t | ƒjdu sJ ‚t | ƒjdu sšJ ‚t | ƒjdu s¤J ‚t | ƒ | ¡d
tt |  ƒ ks·J ‚t | ƒ ¡ | t| ƒ ksÆJ ‚tt | ƒƒt | ƒ ksÔJ ‚tddd} t | ƒjdu säJ ‚t | ƒjdu sîJ ‚t | ƒjdu søJ ‚t | ƒjd u sJ ‚t | ƒ | ¡d
t| ƒ ksJ ‚t | ƒ ¡ t | ƒksJ ‚tt | ƒƒt | ƒks,J ‚tddd} t | ƒjdu s<J ‚t | ƒjdu sFJ ‚t | ƒjdu sPJ ‚t | ƒjdu sZJ ‚t | ƒ ¡ | t| ƒ ksiJ ‚t t| ƒƒdkstJ ‚tt | ƒƒdksJ ‚tddd} t | ƒjdu sJ ‚t | ƒjdu s™J ‚t | ƒjdu s£J ‚t | ƒjdu s­J ‚t | ƒ ¡ | t| ƒ ks¼J ‚t t| ƒƒdksÇJ ‚tt | ƒƒdksÒJ ‚d} t | ƒjdu sÞJ ‚t | ƒjdu sèJ ‚t | ƒjdu sòJ ‚t | ƒjdu süJ ‚t | ƒ ¡ dksJ ‚t t| ƒƒdksJ ‚tt | ƒƒdksJ ‚tdddd}t |ƒjdu s.J ‚t |ƒjdu s8J ‚t |ƒjdu sBJ ‚t |ƒjdu sLJ ‚t |ƒd
 dksWJ ‚t |ƒd jt |ƒdfksgJ ‚t tdddƒjssJ ‚t tdddƒjd u sJ ‚t tdddƒjd u sJ ‚t tdddƒjs›J ‚t tdddƒjd u s©J ‚t tdddƒjd u s·J ‚t tddddƒjd u sÆJ ‚tdddtdƒ} }tdƒ}t | ƒ t¡td| dkfd| dk fdƒksíJ ‚t |ƒ t¡t |ƒksûJ ‚t | ƒ t¡d
t| tdƒd
 d d ksJ ‚t |ƒ t¡t |ƒks!J ‚t |ƒ t¡tdt|dƒf|t|ƒ dfƒks;J ‚t ||ƒƒ t¡tdt||ƒdƒf||ƒt||ƒƒ dfƒks]J ‚t ttt ƒt ƒtju smJ ‚td d!tdƒ  ƒ tdtdƒ ƒ tddtdƒ  ƒ }t |ƒjt u s›t |ƒdks›J ‚dtd
ƒ d
tdƒ  d"td!ƒ  }t |d ƒt!ddƒ }|| }	t |	ƒjt u sÍt |	ƒdksÏJ ‚d S d S )#Ng333333ó?rB   g333333ó¿rC   rG   rQ   r   F)ÚevaluaterD   rH   rN   Trk   Úp©Úpositiver4   ©Únegativerg   r@   r<   )ÚnonzeroÚnz)ry   Úinteger)Únonnegative)Únonpositive)r=   Úzerorf   Úf)r   T)ÚH0é
   r[   é3  )"r   r   Údoitr   r   r   Úsimplifyr   r   Ú	is_finiteÚ
is_complexÚis_imaginaryÚ
is_integerÚis_realÚis_zeror   r^   r%   r   ÚargsÚis_nonnegativeÚis_nonpositiver   r`   r   r&   r   r   r   r   ÚNegativeOneÚfuncr   r	   )
rN   rt   r4   rg   rz   rf   r   ÚeqÚqÚdr7   r7   r8   Ú	test_sign×   sÎ   0($ $&  
ÿ04D :"$*r“   c                  C   sÒ  t d } |  ¡ | dfksJ ‚tdƒ}t|ƒ ¡ t|ƒd t|ƒd  tddƒ ttt|ƒt|ƒƒd ƒ t|ƒd t|ƒd  tddƒ t	tt|ƒt|ƒƒd ƒ fksVJ ‚t
ddd	\}}dt||t  ƒ d  ¡ |d |d  tddƒ tt||ƒd ƒ d tj |d |d  tddƒ t	t||ƒd ƒ d fks¡J ‚t|d ƒ ¡ t|d ƒdfks³J ‚t
d
dd}t|d ƒ ¡ dt|ƒfksÉJ ‚dt dt   ¡ dks×J ‚dt d dt   ¡ dksçJ ‚d S )Néè  r   rN   rD   rB   rH   r;   Tr<   r?   r@   )r   rB   rG   )rk   r   )r   r]   r   r   r   r   r	   r#   r"   r$   r   r   r   r_   Úabs)r4   rN   r5   r6   r?   r7   r7   r8   Útest_as_real_imagQ  s6   
::ÿÿÿÿÿÿ.ýÿ$ $r–   c                  C   s€   t d } t| ƒ}tdƒ}| |  ¡ dksJ ‚t| | ƒdks J ‚| | jd||iddks/J ‚| | jd||iddks>J ‚d S )Nr”   rN   rB   ©Úsubsr   rD   )r   Úintr   Úroundr   r4   )r4   r?   rN   r7   r7   r8   Útest_sign_issue_3068o  s   "r›   c                     sÐ  t tdd„ ƒ tdƒ\‰ } ttˆ ƒƒtˆ ƒksJ ‚tˆ |  ƒjtu s$J ‚tdƒdks,J ‚tdƒdks4J ‚tdƒdks<J ‚ttƒdksDJ ‚tt ƒdksMJ ‚ttƒtu sUJ ‚ttƒt	u s]J ‚ttt
 ƒt
ksgJ ‚tt t
 ƒt
ksrJ ‚ttˆ  ƒtˆ ƒks~J ‚tt ˆ  ƒtˆ ƒks‹J ‚tdˆ  ƒdtˆ ƒ ks™J ‚td	ˆ  ƒd
tˆ ƒ ks§J ‚tdt
 ˆ  |  ƒdt
 tˆ |  ƒ ks½J ‚ttˆ ƒƒtˆ ƒksÉJ ‚ttˆ ƒƒtˆ ƒksÕJ ‚tˆ ƒjddttˆ ƒd tˆ ƒd  ƒksíJ ‚tddd}tdt
 ˆ  | ƒdt
 | tˆ ƒ ks
J ‚tdt
 t ˆ  | ƒdt
 | tˆ ƒ ks#J ‚tddd‰ tddd}td| ƒdks:J ‚ˆ d|  tˆ ƒd|  ksKJ ‚tˆ ƒ ˆ ¡tˆ ƒksYJ ‚tˆ ƒtˆ ƒksdJ ‚tˆ ƒd ˆ d tˆ ƒ ksuJ ‚tˆ ƒd ˆ d ks‚J ‚tˆ ƒd|  jtˆ ƒd| fks–J ‚dtˆ ƒ jtˆ ƒdfks¦J ‚dtˆ ƒd  dˆ d tˆ ƒ  ks»J ‚tˆ ƒd tˆ ƒˆ d  ksÌJ ‚tˆ d ƒˆ d tˆ ƒ ksÝJ ‚ttt ƒtt
 d ƒksíJ ‚tddt  ddt   ƒdtdttddƒƒ ƒ ksJ ‚tddd} tt|  ƒdksJ ‚tdƒ} tt|  ƒtt
 t| ƒ d ƒks4J ‚tddd‰ tˆ ƒ ˆ ¡tˆ ƒ ksIJ ‚tddtdƒ  ƒ tdtdƒ ƒ tddtdƒ  ƒ }t|ƒjtu swt|ƒdkswJ ‚dtdƒ dtdƒ  dtdƒ  }t|d ƒtddƒ }|| }t|ƒjtu s©t|ƒdks©J ‚tdtt
t d ƒ ƒdksºJ ‚tddt  ƒdksÇJ ‚tddt  ƒdtt
ƒ ksØJ ‚tt	ƒt	u sáJ ‚tt	 ƒt	u sëJ ‚tt	t ƒt	u söJ ‚tt	tt	  ƒt	u sJ ‚tddd }td!dd"}tdƒ‰ t|ƒjsJ ‚tˆ ƒjd u s%J ‚t|ƒjd#u s/J ‚tˆ ƒ ¡ tˆ ƒks<J ‚t t‡ fd$d„ƒ ttdt ƒtdt ƒ ƒ}t|ƒ|ks\J ‚tdˆ  ƒdtˆ ƒ kskJ ‚tdˆ d  ƒ}	|	jr‚|	dtˆ d ƒ ks„J ‚tt| ˆ  ƒsŽJ ‚ttˆ ˆ d  ƒsšJ ‚ttˆ |  ƒs¤J ‚td%dd}tˆ | ƒtˆ ƒ| ks¹J ‚tttddd|  ƒsÇJ ‚td&dd}
t|
ˆ ƒd ƒ|
ˆ ƒksÜJ ‚tttd'ƒƒsæJ ‚d S )(Nc                   S   s   t tddƒƒS )NrD   rG   )r   r.   r7   r7   r7   r8   Ú<lambda>~  ó    ztest_Abs.<locals>.<lambda>r:   r   rB   rC   rk   rD   g       Àg       @TrE   r5   ru   rN   r<   r4   ©r{   rG   rH   rQ   rX   r[   é   i9 éùÿÿÿrf   r@   r   r‚   é	   rI   rK   rL   Fc                      s   t ˆ ƒ d¡S )NrD   )r   Úfdiffr7   ©rN   r7   r8   rœ   Ì  r   rt   r   zim(acos(-i + acosh(-g + i))))r2   Ú	TypeErrorr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r^   r•   r‹   r   r!   r	   rb   r¢   r0   r    Úis_Mulr/   r   r   )rf   r5   r4   r   r‘   rt   r’   rK   r   Úer   r7   r£   r8   Útest_Abs}  s¢   ,0.2""
ÿ *"" <(:"$""""r§   c                  C   sø  t ddd} t| ƒ t¡ ¡ }|| t| ƒ | t|  ƒ  ks J ‚dD ]}| | |¡t|ƒks0J ‚q"t dƒ}t|ƒ t¡t|ƒksBJ ‚t dddt dƒ} }t| ƒ t¡t| | dkf|  dfƒksbJ ‚t|ƒ t¡t|ƒksoJ ‚t|ƒ t¡|t|ƒ ks~J ‚t ddd}t|ƒ t¡tt	| t	| dkft	 | dfƒksŸJ ‚t|ƒ t
¡t|t
|ƒ ƒks°J ‚t|ƒ t
¡t|d	  ƒksÀJ ‚t ddd
}ttt	 |  ƒtt	 | ƒ ƒd	  t
¡tt	|  ƒ tt	 | ƒ d	 tt	 |  ƒtt	| ƒ  ksúJ ‚d S )NrN   Tr<   )rk   rC   r   rB   rD   rf   r   r?   r@   rD   ©Úextended_real)r   r   r`   r&   r   r˜   r•   r   r   r   r   r   r   )rN   r5   r?   rf   r7   r7   r8   Útest_Abs_rewriteå  s&   "*6" (8ÿrª   c                  C   sº   t ddd} t| d ƒt| ƒksJ ‚t| d ƒ| d ksJ ‚t ddd} t| d ƒt| ƒks0J ‚t| d ƒ| d ks<J ‚t dddd}t dddd	}t|ƒ|ksRJ ‚t|ƒ| ks[J ‚d S )
NrN   TrE   rD   r<   Únn)r|   r=   Únp)r}   r=   ©r   r   r   )rN   r«   r¬   r7   r7   r8   Útest_Abs_realÿ  s   r®   c            
      C   sl  t dƒ} t| ƒjd u sJ ‚t| ƒjdu sJ ‚t| ƒjd u sJ ‚t| ƒjd u s(J ‚t| ƒjd u s1J ‚t| ƒjd u s:J ‚t| ƒjdu sCJ ‚t ddd}t|ƒjdu sRJ ‚t|ƒjdu s[J ‚t|ƒjd u sdJ ‚t|ƒjd u smJ ‚t|ƒjdu svJ ‚t|ƒjd u sJ ‚t|ƒjdu sˆJ ‚t dddd}t|ƒjdu s˜J ‚t|ƒjdu s¡J ‚t|ƒjd u sªJ ‚t|ƒjdu s³J ‚t|ƒjdu s¼J ‚t|ƒj	du sÅJ ‚t ddd}t|ƒjdu sÔJ ‚t|ƒjdu sÝJ ‚t|ƒjd u sæJ ‚t|ƒjdu sïJ ‚t|ƒj	du søJ ‚t d	dd
}t|ƒjdu sJ ‚t|ƒjdu sJ ‚t|ƒj
d u sJ ‚t|ƒjd u s&J ‚t|ƒjdu s0J ‚t ddd}t|ƒjdu s@J ‚t|ƒj
du sJJ ‚t|ƒjd u sTJ ‚t|ƒjdu s^J ‚t ddd}t dddd}t|ƒjdu suJ ‚t|ƒjdu sJ ‚t|ƒjd u s‰J ‚t ddd}t dddd}	t|ƒjdu s J ‚t|	ƒjdu sªJ ‚t|ƒjd u s´J ‚d S )NrN   T)ÚfiniteÚzF)rF   r~   rt   ru   r‘   )Úrationalr?   rž   r4   )ÚevenÚne)r=   r²   )ÚoddÚno)r=   r´   )r   r   r‰   Úis_extended_realÚis_rationalÚis_positiverŒ   Úis_extended_positiveÚis_extended_nonnegativerŠ   rˆ   Úis_evenÚis_odd)
rN   r   r°   rt   r‘   r?   r¦   r³   Úorµ   r7   r7   r8   Útest_Abs_properties  sd   r¾   c                  C   s4   t ddd} ttd|  d  ƒd|  d ksJ ‚d S )Nr5   Tru   rB   rD   )r   r•   r   )r5   r7   r7   r8   Útest_absM  s   (r¿   c                  C   s>  t dƒtu sJ ‚t dƒdksJ ‚t dƒtksJ ‚t tƒtd ks"J ‚t t ƒt d ks.J ‚t dt ƒtd ks:J ‚t dt ƒttddƒ ksIJ ‚t dt ƒt d ksVJ ‚t tdt t ƒƒdt ksfJ ‚t tdt t ƒƒdt ksvJ ‚t tddt t d  ƒƒttd	dƒ ksJ ‚td
ƒ} t | dƒt| dƒ  ƒ t¡r¢J ‚t	dƒ}t t t |ƒƒƒt
jus³J ‚t t t t |ƒƒƒƒt
ju sÂJ ‚t	ddd}t t |ƒƒt
jusÓJ ‚t t t |ƒƒƒt
ju sàJ ‚tddd}t ||ƒƒdksðJ ‚t dt ||ƒ ƒt dt ƒksJ ‚t	ddd}t |ƒdksJ ‚t |t ƒtd ksJ ‚t	ddd}t |ƒtks.J ‚t |t ƒt d ks<J ‚t	dƒ}tt |ƒƒt |ƒksMJ ‚|t|d   }t |ƒt d|t  ƒksdJ ‚d| dt |d   }t |ƒt dd| t  ƒksJ ‚tddd}|t|  }t |ƒt |dt  ƒksœJ ‚t || ƒt |dt  ƒks­J ‚|t|ƒ tt|ƒ t|ƒ  }t |ƒjd |ksÉJ ‚|d t|d d   }t |ƒjd |ksáJ ‚td
ƒ} d| | dƒd  d| | dƒ  }t |ƒt d| ƒksJ ‚t | dƒƒjt krt | dƒƒj| dƒfksJ ‚d S )Nr   rB   rC   rD   rH   rG   r    rX   rQ   r   rN   r>   Tr¨   rt   )Úextended_positiveru   r4   rw   rk   r<   )r   r   r   r   r	   r   r   Úatomsr   r   r   rd   r   r   r#   r   r   r‹   r   )r   rN   r>   rt   r4   r¦   r7   r7   r8   Útest_argT  s\     ."&"" $6rÂ   c                  C   sZ   t dt ƒtddƒksJ ‚tddd} tddd}t | t|  ƒ t¡t|| ƒks+J ‚d S )NrB   rN   Tr<   rf   )r   r   r"   r   r`   )rN   rf   r7   r7   r8   Útest_arg_rewrite  s   (rÃ   c                  C   s&  t ddd} t ddd}t| ƒ|  ksJ ‚tt|  ƒt|  ks!J ‚t|ƒ|ks)J ‚tt| ƒt | ks6J ‚t| | ƒ| |  ksCJ ‚tt|  | ƒt| |  ksSJ ‚tdƒ\}}tt|ƒƒ|kscJ ‚t|| ƒt|ƒt|ƒ kssJ ‚t|| ƒt|ƒt|ƒ ksƒJ ‚t|| ƒt|ƒt|ƒ ks“J ‚t|| ƒt|ƒt|ƒ ks£J ‚t| ƒt|ƒ ks¯J ‚tddd\}}tt|ƒƒ|ksÁJ ‚t|| ƒt|ƒt|ƒ ksÑJ ‚t|| ƒt|ƒt|ƒ ksáJ ‚t|| ƒt|ƒt|ƒ ksñJ ‚t|| ƒd	t|ƒ t|ƒ ksJ ‚t| ƒt|ƒ ksJ ‚d S )
Nr5   T)Úantihermitianr6   )Ú	hermitianúx yF©ÚcommutativerB   )r   r   r   r   )r5   r6   rN   rf   r7   r7   r8   Útest_adjoint˜  s,           &rÉ   c                  C   sÀ  t ddd} t ddd}t| ƒ| ksJ ‚tt|  ƒt |  ks!J ‚t|ƒ| ks*J ‚tt| ƒt| ks6J ‚t| | ƒ|  | ksCJ ‚tt|  | ƒt|  | ksSJ ‚tdƒ\}}tt|ƒƒ|kscJ ‚t|ƒ ¡ tksmJ ‚t|| ƒt|ƒt|ƒ ks}J ‚t|| ƒt|ƒt|ƒ ksJ ‚t|| ƒt|ƒt|ƒ ksJ ‚t|| ƒt|ƒt|ƒ ks­J ‚t| ƒt|ƒ ks¹J ‚t ddd} t ddd	}t| ƒjsÌJ ‚t|ƒjd u sÕJ ‚t|ƒjd
u sÞJ ‚d S )Nr5   Tr<   r6   r@   rÆ   rI   rK   rL   F)r   r   r   r   Úinverser   rb   )r5   r6   rN   rf   rK   r7   r7   r8   Útest_conjugate³  s*        rË   c                  C   sÖ   t dƒ} tt| ƒƒt| ƒksJ ‚tt| ƒƒt| ƒksJ ‚tt| ƒƒt| ƒks(J ‚tt| ƒƒt| ƒks4J ‚tt| ƒƒt| ƒks@J ‚tt| ƒƒt| ƒksLJ ‚G dd„ dtƒ}|ƒ } t| ƒt| ƒksaJ ‚t| ƒ| ksiJ ‚d S )NrN   c                   @   s$   e Zd Zdd„ Zdd„ Zdd„ ZdS )z+test_conjugate_transpose.<locals>.Symmetricc                 S   ó   d S ©Nr7   ©Úselfr7   r7   r8   Ú_eval_adjoint×  ó   z9test_conjugate_transpose.<locals>.Symmetric._eval_adjointc                 S   rÌ   rÍ   r7   rÎ   r7   r7   r8   Ú_eval_conjugateÚ  rÑ   z;test_conjugate_transpose.<locals>.Symmetric._eval_conjugatec                 S   s   | S rÍ   r7   rÎ   r7   r7   r8   Ú_eval_transposeÝ  rÑ   z;test_conjugate_transpose.<locals>.Symmetric._eval_transposeN)Ú__name__Ú
__module__Ú__qualname__rÐ   rÒ   rÓ   r7   r7   r7   r8   Ú	SymmetricÖ  s    r×   )r   r   r   r   r   )rN   r×   r7   r7   r8   Útest_conjugate_transposeÍ  s   	rØ   c                  C   s°  t ddd} t| ƒ| ksJ ‚tt|  ƒt|  ksJ ‚tdƒ\}}tt|ƒƒ|ks*J ‚t|| ƒt|ƒt|ƒ ks:J ‚t|| ƒt|ƒt|ƒ ksJJ ‚t|| ƒt|ƒt|ƒ ksZJ ‚t|| ƒt|ƒt|ƒ ksjJ ‚t| ƒt|ƒ ksvJ ‚tddd\}}tt|ƒƒ|ksˆJ ‚t|| ƒt|ƒt|ƒ ks˜J ‚t|| ƒt|ƒt|ƒ ks¨J ‚t|| ƒt|ƒt|ƒ ks¸J ‚t|| ƒdt|ƒ t|ƒ ksÊJ ‚t| ƒt|ƒ ksÖJ ‚d S )Nr5   TrE   rÆ   FrÇ   rB   )r   r   r   r   )r5   rN   rf   r7   r7   r8   Útest_transposeä  s"          $rÙ   c            
   	   C   s’  ddl m} m} tdƒ}tddd}tdƒ}i }|dƒ| dƒ|fks$J ‚|d	t ƒ| d	t ƒ|fks4J ‚|t|ƒd
dt|ƒksBJ ‚|d	| d
dd	| ksPJ ‚||tƒ| d
d|| tƒƒ| ksdJ ‚||dd| |ƒkspJ ‚||dd|kszJ ‚|||ƒdd|| |ƒƒksŠJ ‚|d	| dd| d	| ƒksšJ ‚|d	||ƒ dd| d	|| |ƒƒ ƒks°J ‚|||ƒ| ƒ\}}| |¡||ƒ| ksÇJ ‚tdƒ}tddd}	|tt	dƒ| t| | d  d|	d   ƒ dt	t
ƒ |	  |t tfƒddtt	dƒ|	tdƒ ttt
 ƒ  t|	tdƒ dttt
 ƒ  ttt
 ƒ | | | ƒdtdƒ   d ƒ tdƒ | |ƒ dt	t
ƒ  |t tfƒksGJ ‚d S )Nr   )Ú
polar_liftÚpolarifyrN   r°   T)Úpolarr   rC   rB   Fr—   )ÚliftÚmuÚsigmaru   rD   )Ú$sympy.functions.elementary.complexesrÚ   rÛ   r   r   r   r   r˜   r'   r   r   r   r   )
rÚ   rÛ   rN   r°   r   ÚESÚnewexr˜   rÞ   rß   r7   r7   r8   Útest_polarifyú  sR    (  ,<
ÿþ 4
ÿÿÿþþ
þ
þþrã   c                  C   sÜ  ddl m} m}m} ddlm} ddlm} ddlm	} ddl
m}m} ddlm} tdt ƒd	 }	tdt ƒd	 }
|d	ƒd	ksBJ ‚||	ƒ|
ksJJ ‚||	d
 ƒ|
d
 ksVJ ‚||	| ƒ|	| ksbJ ‚||	| ƒ|
| ksnJ ‚||	| ƒ|
| kszJ ‚|tt|	ƒƒƒtt|
ƒƒksŠJ ‚||d
t ƒ}||ƒ|ks™J ‚|t|ƒƒt|ƒks¥J ‚||	|	 dd|	|
 ks³J ‚||||	|	 ƒƒ|||	|
 ƒksÅJ ‚|t|	ƒƒt|
ƒksÑJ ‚|||	ƒƒ||
ƒksÝJ ‚|||	ƒƒ||
ƒkséJ ‚|||	ƒƒ||
ƒksõJ ‚||||	ƒƒ|||	ƒksJ ‚||t|	ƒt|	tdƒ ƒƒƒ|t|
ƒt|
d	 ƒƒks!J ‚||| dƒd
tdƒ ƒƒ|dd
ƒks6J ‚|t|	dƒƒt|
dƒksEJ ‚|||	dƒƒ||
dƒksTJ ‚|| |ƒdkƒ|dkkscJ ‚|dƒdu slJ ‚d S )Nr   )rÚ   Úprincipal_branchÚ
unpolarify)ÚNe)Útanh)Úerf)ÚgammaÚ
uppergammar£   rŸ   rB   rD   T)Úexponents_only)rà   rÚ   rä   rå   Úsympy.core.relationalræ   Ú%sympy.functions.elementary.hyperbolicrç   Ú'sympy.functions.special.error_functionsrè   Ú'sympy.functions.special.gamma_functionsré   rê   Ú	sympy.abcrN   r   r   r   r   r$   r   r   )rÚ   rä   rå   ræ   rç   rè   ré   rê   rN   rt   ÚurK   r7   r7   r8   Útest_unpolarify  sF    $
ÿ
ÿrò   c                  C   s`   t dƒ} t| ƒjddt| ƒksJ ‚t| ƒjddt| ƒks J ‚t| ƒjddt| ƒks.J ‚d S )NrN   T)Útrig)r   r   r   r   r   r£   r7   r7   r8   Útest_issue_4035M  s    rô   c                  C   s$   t dƒ} tt| ƒƒt| ƒksJ ‚d S )NrN   )r   r   r£   r7   r7   r8   Útest_issue_3206T  s   rõ   c                  C   sv   t ddd} t ddd}tdƒ}|| ƒ ¡  | ¡|| ƒ | ¡ ¡ ks$J ‚||ƒ ¡  |¡||ƒ |¡ ¡  ks9J ‚d S )NrN   Tr<   rf   r@   r   )r   r   r   r^   ©rN   rf   r   r7   r7   r8   Ú$test_issue_4754_derivative_conjugateY  s
   (.r÷   c                  C   sÚ  t ddd} t ddd}tdƒ}t|| ƒƒ | ¡t|| ƒ | ¡ƒks$J ‚t|| ƒƒ | ¡t|| ƒ | ¡ƒks8J ‚t||ƒƒ |¡t t||ƒ |¡ƒ ksOJ ‚t||ƒƒ |¡t t||ƒ |¡ƒ ksfJ ‚t|| ƒƒ | ¡ || ƒdt|   ¡ ¡ | t	d| d  ƒ ks‡J ‚t
|| ƒƒ | ¡ || ƒdt| d   ¡ ¡ d|  d| d	   ksªJ ‚t||ƒƒ |¡ ||ƒd| ¡ ¡ | t	d|d  ƒ ksÊJ ‚t
||ƒƒ |¡ ||ƒt|d  ¡ ¡ d| d|d	   ksëJ ‚d S )
NrN   Tr<   rf   r@   r   rB   rD   rH   )r   r   r   r^   r   r   r   r˜   rƒ   r   r   rö   r7   r7   r8   Útest_derivatives_issue_4757a  s   ((..BF@Frø   c               	   C   sP  ddl m}  tdƒ}tdƒ}tdƒ}t|g|g|ggƒ}| ¡ }|t|tt|ƒd t|ƒd  t|ƒd  ƒ g|tt|ƒd t|ƒd  t|ƒd  ƒ g|tt|ƒd t|ƒd  t|ƒd  ƒ ggƒksjJ ‚t|d |d |d  |d   |d |d |d  |d    |d |d |d  |d    ƒ|_| |jƒdks¦J ‚d S )Nr   ©r„   Úv0Úv1Úv2rD   rB   )Úsympy.simplify.simplifyr„   r   r(   Ú
normalizedr   r   Únorm)r„   rú   rû   rü   ÚVÚUr7   r7   r8   Útest_issue_11413o  s   ,,,ýfr  c                  C   s(  ddl m} m}m}m} tdƒ}tddd}|dt ƒ| dt tƒks%J ‚|d| ƒ| d| tƒks4J ‚t|dt d ƒt	d ƒsCJ ‚t|dt d ƒt	 d ƒsSJ ‚t| dt d d	t	 ƒt	d ƒseJ ‚t| dt d d	t	 ƒt	 d ƒsxJ ‚|||t	ƒƒ| |t	ƒks†J ‚||dt ƒƒ|dt ƒks–J ‚| |dt ƒdt	 ƒ| dt dt	 ƒks¬J ‚| |dt ƒd	t	 ƒ| dt d	t	 ƒksÂJ ‚| |dt ƒt	ƒ| |dt ƒt	ƒksÖJ ‚||dt ƒƒt	d
 ksäJ ‚| d| |ƒ| ||ƒksòJ ‚| t	| |ƒ| ||ƒksJ ‚t
|dt ƒƒt
dt ƒksJ ‚d S )Nr   )Úperiodic_argumentrÚ   rä   Úunbranched_argumentrN   rt   Tru   rD   rB   rG   rH   )rà   r  rÚ   rä   r  r   r   r   r9   r   r   )r  rÚ   rä   r  rN   rt   r7   r7   r8   Útest_periodic_argument~  s4    $&ÿ ÿÿÿ&r  c                  C   s0   ddl m}  t| dt d td ƒdƒsJ ‚d S )Nr   ©rä   rB   rD   )rà   rä   r9   r   r   r  r7   r7   r8   Útest_principal_branch_failœ  s   $r  c                  C   sN  ddl m} m} tddd}tdƒ}tddd}|| |ƒ|ƒ|||ƒks&J ‚|| dt ƒ|ƒ|dt |ƒks8J ‚|d| |ƒd|||ƒ ksHJ ‚|d	tƒtdƒksSJ ‚|d
dt ƒttt ƒksbJ ‚|d
tƒtdƒksmJ ‚|tdt t ƒ| dt ƒ|ttt ƒ| dt ƒks‹J ‚||ttt ƒ dt ƒ|tt t ƒ ks£J ‚|tt t d ƒ| |ƒ dt ƒtt t d ƒ| ksÂJ ‚t|d	t d dt ƒdt ƒsÔJ ‚t|d	t d dt ƒdt ƒsæJ ‚t|d	t d d	t ƒdt ƒsøJ ‚||tƒj|u sJ ‚||dƒj|u sJ ‚||t	 ƒj|u sJ ‚||t
ƒj|u s%J ‚d S )Nr   )rÚ   rä   rt   Tru   rN   rw   rD   rB   rC   rG   éüÿÿÿ)rà   rÚ   rä   r   r   r   r   r9   r   r   r   )rÚ   rä   rt   rN   Únegr7   r7   r8   Útest_principal_branch£  s0   $ ÿ0"ÿ$$$r
  c            	      C   sÐ   t d } t| ƒ}t| | ƒdksJ ‚t| | ƒ| | ksJ ‚tdƒ}t d }t d }t|ƒd t|ƒd  }|| | | }ddlm} t||ƒƒdksNJ ‚dd	dt	dd
ƒfD ]}t| 
||¡ƒdkseJ ‚qWd S )Nr”   rB   rN   i$úÿÿrD   r   rù   éo   é   r   )r   r™   r   r•   r   r#   r$   rý   r„   r	   r˜   )	r4   r?   rN   ÚepsÚbigÚoner¦   r„   Úxir7   r7   r8   Útest_issue_6167_6151Á  s   ÿr  c                  C   s\   ddl m}  tdddƒ}| |d ƒ|d ksJ ‚| |d |d  ƒ|d |d  ks,J ‚d S )Nr   )rå   rP   rD   )r   r   )rB   r   )rà   rå   r*   )rå   rP   r7   r7   r8   Útest_issue_14216Ò  s   ,r  c                  C   s6   t ddd} t| td| dkfd|  dfƒ ƒsJ ‚d S )Nr>   Tr<   r   rB   )r   r   r   )r>   r7   r7   r8   Útest_issue_14238Ù  s   *r  c                  C   sL   t dƒ} tdd|   ƒd d|  fD ]}t|ƒt| ƒ dks#J |ƒ‚qd S )NrN   rŸ   rD   rB   r   r­   )rN   r5   r7   r7   r8   Útest_issue_22189ß  s     ÿr  c                  C   s˜   t dddd} t ddd}t dddd}t| ƒjd u sJ ‚t| ƒjdu s&J ‚t|ƒjd u s/J ‚t|ƒjd u s8J ‚t|ƒjdu sAJ ‚t|ƒjd u sJJ ‚d S )	NÚnonrealFT)r=   r¯   Únonimaginaryr@   Únonzerononimaginary)r~   rA   )r   r   rŠ   r   )ÚnrÚniÚnznir7   r7   r8   Útest_zero_assumptionså  s   r  c                  C   sJ   t ddd} tddd}tt| |ƒƒ| |ƒƒ}| ¡ t| |ƒƒks#J ‚d S )Nr   Tr<   rN   )r   r   r   r   rƒ   r   )r   rN   r   r7   r7   r8   Útest_issue_15893õ  s   r  N)gÚsympy.core.exprr   Úsympy.core.functionr   r   r   r   Úsympy.core.numbersr   r   r	   r
   r   r   r   r   rì   r   Úsympy.core.singletonr   Úsympy.core.symbolr   r   rà   r   r   r   r   r   r   r   r   Ú&sympy.functions.elementary.exponentialr   r   r   Ú(sympy.functions.elementary.miscellaneousr   Ú$sympy.functions.elementary.piecewiser   Ú(sympy.functions.elementary.trigonometricr    r!   r"   r#   r$   Ú'sympy.functions.special.delta_functionsr%   r&   Úsympy.integrals.integralsr'   Úsympy.matrices.denser(   Ú%sympy.matrices.expressions.funcmatrixr)   Ú"sympy.matrices.expressions.matexprr*   Úsympy.matrices.immutabler+   r,   Úsympy.matricesr-   Úsympy.sets.setsr.   r/   r0   Úsympy.testing.pytestr1   r2   r3   r9   rj   rr   r“   r–   r›   r§   rª   r®   r¾   r¿   rÂ   rÃ   rÉ   rË   rØ   rÙ   rã   rò   rô   rõ   r÷   rø   r  r  r  r
  r  r  r  r  r  r  r7   r7   r7   r8   Ú<module>   sx    ((`Yz
h<<
#/

